Growth has fallen in the U.S., while firm concentration and profits have risen. Meanwhile, labor’s share of national income is down, mostly due to the rising market share of low labor share firms. We propose a theory for these trends in which the driving force is falling firm-level costs of spanning multiple markets, perhaps due to accelerating IT advances. In response, the most efficient firms spread into new markets, thereby generating a temporary burst of growth. Because their efficiency is difficult to imitate, less efficient firms find their markets more difficult to enter profitably and innovate less. Even the most efficient firms do less innovation eventually because they are more likely to compete with each other if they try to expand further.
Across cohorts of firms and plants within the U.S., Indonesia, India and
China, we find that average discounted profits rise systematically with average labor productivity at the time of entry. The number of entrants, in
contrast, is weakly connected to average labor productivity but closely tied
to aggregate employment. In many models of firm dynamics, growth, and
trade, these facts imply that the cost of creating a new business is increasing with average productivity given a zero profit condition for entrants. Entry costs could rise as development proceeds because entry is laborintensive and/or because it is more expensive to set up firms using more skilled workers and more sophisticated technology.
This paper investigates the quantitative importance of financial frictions on aggregate productivity using a panel of young and unlisted firms in Japan. I find that firm leverage and output-to-capital ratios rise with firm productivity controlling for firm asset, age and cohort. I use these facts in indirect inference to estimate a standard general equilibrium model with financial frictions. The model matches the facts the best when borrowing limits rise with both firm asset and productivity. Compared to the common assumption that borrowing limits rise only with assets, aggregate productivity loss due to financial frictions is one-third smaller.
We study the asymptotic distribution of simulation estimators, where the same set of draws are used for all observations under general conditions that do not require the function used in the simulation to be smooth. We consider two cases: estimators that solve a system of equations involving simulated moments and estimators that maximize a simulated likelihood. Many simulation estimators used in empirical work involve both overlapping simulation draws and non-differentiable moment functions. Developing sampling theorems under these two conditions provides an important complement to the existing results in the literature on the asymptotics of simulation estimators.
Published Articles (Refereed Journals and Volumes)
We derive the asymptotic distribution of the parameters of the Berry et al. (1995, BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that, as long as the number of simulation draws R and the number of markets T approach infinity, our estimator is √m = √min(R,T) consistent and asymptotically normal. We do not impose any relationship between the rates at which R and T go to infinity, thus allowing for the case of R < < T. We provide a consistent estimate of the asymptotic variance which can be used to form asymptotically valid confidence intervals. Instead of directly minimizing the BLP GMM objective function, we propose using Hamiltonian Markov chain Monte Carlo methods to implement a Laplace-type estimator which is asymptotically equivalent to the GMM estimator.
This paper derives explicit error bounds for numerical policies of η-concave stochastic dynamic programming problems, without assuming the optimal policy is interior. We demonstrate the usefulness of our error bound by using it to pinpoint the states at which the borrowing constraint binds in a widely used income fluctuation problem with standard calibrations and a firm production problem with financial constraints.
Solving the Income Fluctuation Problem with Unbounded Rewards
Journal of Economic Dynamics and Control 45, August 2014, 353-365 | With Stachurski
This paper studies the income fluctuation problem without imposing bounds on utility, assets,
income or consumption. We prove that the Coleman operator is a contraction mapping over the
natural class of candidate consumption policies when endowed with a metric that evaluates
consumption differences in terms of marginal utility. We show that this metric is complete,
and that the fixed point of the operator coincides with the unique optimal policy. As a
consequence, even in this unbounded setting, policy function iteration always converges to the
optimal policy at a geometric rate.
Generalized Look-Ahead Methods for Computing Stationary Densities
Mathematics of Operations Research Publication 37 (3), August 2008, 489-500 | With Braun and Stachurski
The look-ahead estimator is used to compute densities associated with Markov processes via simulation. We study a framework that extends the look-ahead estimator to a broader range of applications. We provide a general asymptotic theory for the estimator, where both L_1 consistency and L_2 asymptotic normality are established. The L_2 asymptotic normality implies root-n convergence rates for L_2 deviation.
Slowing growth of total factor productivity has led some to suggest that the world is running out of ideas for innovation. This column suggests that the way output is measured is vital to assessing this, and quantifies the role of imputation in output measurement bias. By differentiating between truly ‘new’ and incumbent products, it finds missing growth in the US economy. Accounting for this missing growth will allow statistical offices to improve their methodology and more readily recognise the ready availability of new ideas, but also has implications for optimal growth and inflation targeting policies.